Terms up to relative order \(1/N_c^3\)  in the \(1/N_c\)  expansion from the above expressions have been evaluated for spin-independent and spin-dependent contributions in Refs. [1]} and [2]}, respectively. Terms that participate to the next relative order, \(1/N_c^4\) , for instance \(\mathcal {D}_3^{ia} \mathcal {O}_3^{ia}\)  or \(\mathcal {D}_3^{ia} J^2 \mathcal {D}_3^{ia}\) , would complete the calculation for \(N_c=3\)  so they are evaluated and listed in Appendix  for the sake of completeness.
